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Simplifying (500 + x) * x = 50 Reorder the terms for easier multiplication: x(500 + x) = 50 (500 * x + x * x) = 50 (500x + x2) = 50 Solving 500x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 500x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 500x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 500x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 500x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 500x + x2 = 0 + 50 500x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 500x + x2 = 50 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = 50 + 62500 Reorder the terms: 62500 + 500x + x2 = 50 + 62500 Combine like terms: 50 + 62500 = 62550 62500 + 500x + x2 = 62550 Factor a perfect square on the left side: (x + 250)(x + 250) = 62550 Calculate the square root of the right side: 250.099980008 Break this problem into two subproblems by setting (x + 250) equal to 250.099980008 and -250.099980008.Subproblem 1
x + 250 = 250.099980008 Simplifying x + 250 = 250.099980008 Reorder the terms: 250 + x = 250.099980008 Solving 250 + x = 250.099980008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 250.099980008 + -250 Combine like terms: 250 + -250 = 0 0 + x = 250.099980008 + -250 x = 250.099980008 + -250 Combine like terms: 250.099980008 + -250 = 0.099980008 x = 0.099980008 Simplifying x = 0.099980008Subproblem 2
x + 250 = -250.099980008 Simplifying x + 250 = -250.099980008 Reorder the terms: 250 + x = -250.099980008 Solving 250 + x = -250.099980008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -250.099980008 + -250 Combine like terms: 250 + -250 = 0 0 + x = -250.099980008 + -250 x = -250.099980008 + -250 Combine like terms: -250.099980008 + -250 = -500.099980008 x = -500.099980008 Simplifying x = -500.099980008Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.099980008, -500.099980008}
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